in this paper we present some results about subgroup which is generalization of the subgroup $r_{2}^{otimes}(g)={ain g|[a,g]otimes g=1_{otimes},forall gin g}$ of right $2_{otimes}$-engel elements of a given group $g$. if $p$ is an odd prime, then with the help of these results, we obtain the results about tensor squares of p-groups satisfying the law $[x,g,y]otimes g=1_{otimes}$, for all $x, g,...

where E ( K ) is the energy spectrum function, K is the wave-number magnitude, and C is a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covariance Rij(r) are O ( r 3 ) for large values of the separation magnitude r. An argument based on the conserv...

We address the problem of multiple view stereo from a perceptual organization perspective. Currently, the leading methods in the field are volumetric. They operate at the level of scene voxels and image pixels, without considering the structures depicted in them. On the other hand, many perceptual organization methods for binocular stereo are not extensible to more images. We present an approac...

In 2 experiments, participants haptically estimated length and heaviness of handheld rods while wielding without seeing them. The sets of rods had been constructed such that variation of static moment and the 1st eigenvalue of the inertia tensor (I1) were separated. Consistent with previous findings, perceived rod length correlated strongly with I1. However, multiple regressions on current data...

In this paper, we propose the canonical correlation kernel (CCK), that seamlessly integrates the advantages of lower dimensional representation of videos with a discriminative classifier like SVM. In the process of defining the kernel, we learn a low-dimensional (linear as well as nonlinear) representation of the video data, which is originally represented as a tensor. We densely compute featur...

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression i...

The energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. Fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

The emphasis of this review is both the geometric realization 2-point velocity correlation tensor field Bij (x,x′,t) and isometries space K3 equipped with a (pseudo-) Riem...

When an n -partite physical system is measured by observers, the joint probabilities of outcomes conditioned on observables chosen parties form a nonnegative tensor, called correlation tensor (CT). In this paper, we aim to establish some characterizations nonsignaling and Bell locality CT, respectively. By placing CTs within linear space correlation-type tensors (CTTs), prove that every CTT can...

For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly m...